Topological Link Models of Multipartite Entanglement

Ning Bao; Newton Cheng; Sergio Hernández-Cuenca; Vincent Paul Su

doi:10.22331/q-2022-06-20-741

Topological Link Models of Multipartite Entanglement

Ning Bao¹, Newton Cheng², Sergio Hernández-Cuenca³, and Vincent Paul Su²

¹Computational Science Initiative, Brookhaven National Lab, Upton, NY, 11973, USA
²Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720, USA
³Department of Physics, University of California, Santa Barbara, CA 93106, USA

Published:	2022-06-20, volume 6, page 741
Eprint:	arXiv:2109.01150v2
Doi:	https://doi.org/10.22331/q-2022-06-20-741
Citation:	Quantum 6, 741 (2022).

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Abstract

We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory.

► BibTeX data

@article{Bao2022topologicallink,
  doi = {10.22331/q-2022-06-20-741},
  url = {https://doi.org/10.22331/q-2022-06-20-741},
  title = {Topological {L}ink {M}odels of {M}ultipartite {E}ntanglement},
  author = {Bao, Ning and Cheng, Newton and Hern{\'{a}}ndez-Cuenca, Sergio and Su, Vincent Paul},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {741},
  month = jun,
  year = {2022}
}

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Cited by

[1] Sergio Hernández-Cuenca, Veronika E. Hubeny, and Massimiliano Rota, "The holographic entropy cone from marginal independence", Journal of High Energy Physics 2022 9, 190 (2022).

[2] Temple He, Sergio Hernández-Cuenca, and Cynthia Keeler, "Beyond the Holographic Entropy Cone via Cycle Flows", Communications in Mathematical Physics 405 11, 252 (2024).

[3] Vijay Balasubramanian and Charlie Cummings, "Multipartite entanglement structure of fibered link states", Physical Review D 111 10, 105020 (2025).

[4] Dmitry Melnikov, "Entanglement classification from a topological perspective", Physical Review D 107 12, 126005 (2023).

[5] Charlie Cummings, "Entanglement in typical states of Chern-Simons theory", Physical Review D 112 2, 025014 (2025).

[6] Ning Bao and Joydeep Naskar, "Properties of the contraction map for holographic entanglement entropy inequalities", Journal of High Energy Physics 2024 6, 39 (2024).

[7] Temple He, Jaeha Lee, and Hirosi Ooguri, "Exploring the holographic entropy cone via reinforcement learning", Journal of High Energy Physics 2026 6, 267 (2026).

[8] Ning Bao, Keiichiro Furuya, and Joydeep Naskar, "On the completeness of contraction map proof method for holographic entropy inequalities", Journal of High Energy Physics 2025 12, 140 (2025).

[9] Sergio Hernández-Cuenca, Veronika E. Hubeny, and Hewei Frederic Jia, "Holographic entropy inequalities and multipartite entanglement", Journal of High Energy Physics 2024 8, 238 (2024).

[10] Ning Bao, Keiichiro Furuya, and Joydeep Naskar, "Towards a complete classification of holographic entropy inequalities", Journal of High Energy Physics 2025 3, 117 (2025).

[11] Brianna Grado-White, Guglielmo Grimaldi, Matthew Headrick, and Veronika E. Hubeny, "Testing holographic entropy inequalities in 2 + 1 dimensions", Journal of High Energy Physics 2025 1, 65 (2025).

[12] William Munizzi and Howard J. Schnitzer, "Entropy cones and entanglement evolution for Dicke states", Physical Review A 109 1, 012405 (2024).

[13] Guglielmo Grimaldi, Matthew Headrick, and Veronika E. Hubeny, "A new characterization of the holographic entropy cone", SciPost Physics 20 4, 122 (2026).

[14] Matteo Fadel and Sergio Hernández-Cuenca, "Symmetrized holographic entropy cone", Physical Review D 105 8, 086008 (2022).

[15] William Munizzi, "Bit by Bit: Gravity Through the Lens of Quantum Information", arXiv:2406.01695, (2024).

[16] Howard J. Schnitzer, "The entropy cones of $W_N$ and $W_N^d$ states", arXiv:2204.04532, (2022).

[17] C. J. Ramírez-Valdez, H. García-Compeán, and J. de-la-Cruz-Moreno, "Further Remarks on the Entanglement Entropy of Hopf links", arXiv:2408.13439, (2024).

[18] Temple He, Jaeha Lee, and Hirosi Ooguri, "Exploring the holographic entropy cone via reinforcement learning", arXiv:2601.19979, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-08 17:52:05) and SAO/NASA ADS (last updated successfully 2026-08-08 17:52:06). The list may be incomplete as not all publishers provide suitable and complete citation data.

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